Purpose

This study aims to investigate the dual solutions for axisymmetric flow and heat transfer due to a permeable radially shrinking disk in copper oxide (CuO) and silver (Ag) hybrid nanofluids with radiation effect.

Design/methodology/approach

The partial differential equations that governed the problem will undergo a transformation into a set of similarity equations. Following this transformation, a numerical solution will be obtained using the boundary value problem solver, bvp4c, built in the MATLAB software. Later, analysis and discussion are conducted to specifically examine how various physical parameters affect both the flow characteristics and the thermal properties of the hybrid nanofluid.

Findings

Dual solutions are discovered to occur for the case of shrinking disk (λ < 0). Stronger suction triggers the critical values’ expansion and delays the boundary layer separation. Through stability analysis, it is determined that one of the solutions is stable, whereas the other solution exhibits instability, over time. Moreover, volume fraction upsurge enhances skin friction and heat transfer in hybrid nanofluid. The hybrid nanofluid’s heat transfer also heightened with the influence of radiation.

Originality/value

Flow over a shrinking disk has received limited research focus, in contrast to the extensively studied axisymmetric flow problem over a diverse set of geometries such as flat surfaces, curved surfaces and cylinder. Hence, this study highlights the axisymmetric flow due to a shrinking disk under radiation influence, using hybrid nanofluids containing CuO and Ag. Upon additional analysis, it is evidently shows that only one of the solutions exhibits stability, making it a physically dependable choice in practical applications. The authors are very confident that the findings of this study are novel, with several practical uses of hybrid nanofluids in modern industry.

中文翻译：

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由于具有辐射效应的氧化铜 (CuO) 和银 (Ag) 混合纳米流体中的可渗透径向收缩盘，可实现轴对称流动和传热的双重解决方案

目的

本研究旨在研究氧化铜（CuO）和银（Ag）混合纳米流体中具有辐射效应的可渗透径向收缩盘导致轴对称流动和传热的双重解决方案。

设计/方法论/途径

控制问题的偏微分方程将转换为一组相似方程。在此转换之后，将使用 MATLAB 软件中内置的边值问题求解器 bvp4c 获得数值解。随后，进行了分析和讨论，具体研究了各种物理参数如何影响混合纳米流体的流动特性和热性能。

发现

发现对于收缩盘 ( λ < 0)的情况会出现对偶解。更强的吸力会触发临界值的膨胀并延迟边界层分离。通过稳定性分析，可以确定随着时间的推移，其中一个解是稳定的，而另一个解则表现出不稳定。此外，体积分数的增加增强了混合纳米流体中的表面摩擦和传热。混合纳米流体的传热也因辐射的影响而增强。

原创性/价值

与广泛研究的各种几何形状（例如平面、曲面和圆柱体）上的轴对称流动问题相比，收缩盘上的流动受到的研究重点有限。因此，本研究使用含有 CuO 和 Ag 的混合纳米流体，强调了由于辐射影响下圆盘收缩而导致的轴对称流动。经过进一步的分析，很明显，只有一种解决方案表现出稳定性，使其成为实际应用中物理上可靠的选择。作者非常有信心这项研究的结果是新颖的，混合纳米流体在现代工业中具有多种实际用途。